A modified ARMA model is proposed for the simulations of slowly varying drift forces in short crested waves from a given force spectrum for the sake of improving calculational time of drift forces. Herein, the property of non-Gaussian distribution of drift forces is considered and the results of the calulations are compared with those obtained by the drift force formula which is derived by Pinkster. It is shown that a lower order ARMA model and suitable time increment can bring about good precision of simulation. Numerical calculations by the modified ARMA model and the drift force formula give almost the same results in spectral analysis. In addition, by statistical analysis of the drift forces, the probability density functions of the forces indicate different in direction of drift forces. The drift forces simulated by two methods show little different probability density function in surge direction, but almost the same in sway and yaw direction. Furthermore, the computational efficiency and applicability of the modified ARMA model are discussed by conducting simulations of low frequency motions of moored tanker of FPSO. It is revealed that the modified ARMA model can be accepted. The numerical simulations based on modified ARMA model and drift formula are in agreement with each other in spectra of motion responses. In computational time, ARMA model is very short. On the other hand, the simulations by drift force formula take too long time to put practical use.